“If you cannot calculate, you cannot speculate on future pleasures and your life will not be that of a human, but that of an oyster or a jellyfish.” -Plato, Philebus, as quoted by Georges Ifrah in The Universal History of Computing: From the abacus to the quantum computer

Before I begin describing how to use an abacus, I ought to specify that there really is not just one, quintessential abacus. In general, there are three types of abaci: dust, counter, and frame. (These categories are suggested in passing by Gardner, Smith, and Williams, but I would like to establish them formally in my final paper.) The dust abacus was a dustboard (defined in post) with columns for place value marked, and Hindu numerals (excluding zero) written in these columns (Ifrah, 2000). This method is only a few steps from the modern pen-and-paper method.

“Accurate reckoning. The entrance into the knowledge of all existing things and all obscure secrets.” –Introduction to the Rhind Mathematical Papyrus (as quoted by Victor J. Katz in A History of Mathematics: Brief Version)

“Machines, too simple to get out of order, are they not more trustworthy than the average human brain crowded nowadays with the perplexities of modern civilization?” –Rikitaro Fujisawa in the Appendix (1912) to The Development of Mathematics in China and Japan